Space of modular forms of level 2550 and weight 2

• Label: 2550.2
• Level: 2550
• Weight: 2
• Dimension: 39542
• Nonzero newspaces: 36
• Sturm bound: 691200
• Trace bound: 28

Defining parameters

Level:	\( N \)	=	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(691200\)
Trace bound:			\(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2550))\).

	Total	New	Old
Modular forms	176384	39542	136842
Cusp forms	169217	39542	129675
Eisenstein series	7167	0	7167

Trace form

39542 * q - 6 * q^2 - 14 * q^3 - 6 * q^4 - 20 * q^5 - 14 * q^6 - 48 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 - 40 * q^11 + 10 * q^12 - 52 * q^13 - 16 * q^14 + 8 * q^15 - 14 * q^16 + 2 * q^17 + 14 * q^18 + 72 * q^19 + 16 * q^20 + 16 * q^21 + 88 * q^22 + 80 * q^23 + 18 * q^24 + 172 * q^25 - 12 * q^26 - 14 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 - 32 * q^31 + 14 * q^32 + 8 * q^33 + 28 * q^34 + 16 * q^35 - 6 * q^36 - 16 * q^37 - 24 * q^38 + 108 * q^39 + 12 * q^40 - 52 * q^41 + 64 * q^42 + 104 * q^43 - 40 * q^44 + 140 * q^45 + 48 * q^46 + 64 * q^47 + 18 * q^48 + 126 * q^49 - 36 * q^50 + 94 * q^51 - 20 * q^52 + 40 * q^53 + 42 * q^54 + 48 * q^55 - 16 * q^56 + 112 * q^57 - 116 * q^58 - 72 * q^59 - 64 * q^60 - 196 * q^61 - 96 * q^62 - 168 * q^63 - 6 * q^64 - 148 * q^65 - 88 * q^66 - 248 * q^67 + 50 * q^68 - 168 * q^69 + 160 * q^70 + 368 * q^71 + 18 * q^72 + 892 * q^73 + 436 * q^74 - 72 * q^75 + 8 * q^76 + 672 * q^77 + 212 * q^78 + 736 * q^79 + 108 * q^80 - 46 * q^81 + 828 * q^82 + 600 * q^83 + 88 * q^84 + 734 * q^85 + 408 * q^86 + 596 * q^87 + 408 * q^88 + 664 * q^89 - 76 * q^90 + 1344 * q^91 + 176 * q^92 + 552 * q^93 + 736 * q^94 + 480 * q^95 + 18 * q^96 + 836 * q^97 + 354 * q^98 + 224 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2550))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
2550.2.a	\(\chi_{2550}(1, \cdot)\)	2550.2.a.a	1	1
		2550.2.a.b	1
		2550.2.a.c	1
		2550.2.a.d	1
		2550.2.a.e	1
		2550.2.a.f	1
		2550.2.a.g	1
		2550.2.a.h	1
		2550.2.a.i	1
		2550.2.a.j	1
		2550.2.a.k	1
		2550.2.a.l	1
		2550.2.a.m	1
		2550.2.a.n	1
		2550.2.a.o	1
		2550.2.a.p	1
		2550.2.a.q	1
		2550.2.a.r	1
		2550.2.a.s	1
		2550.2.a.t	1
		2550.2.a.u	1
		2550.2.a.v	1
		2550.2.a.w	1
		2550.2.a.x	1
		2550.2.a.y	1
		2550.2.a.z	1
		2550.2.a.ba	1
		2550.2.a.bb	1
		2550.2.a.bc	1
		2550.2.a.bd	1
		2550.2.a.be	1
		2550.2.a.bf	1
		2550.2.a.bg	2
		2550.2.a.bh	2
		2550.2.a.bi	2
		2550.2.a.bj	2
		2550.2.a.bk	2
		2550.2.a.bl	2
		2550.2.a.bm	2
		2550.2.a.bn	3
		2550.2.a.bo	3
2550.2.c	\(\chi_{2550}(1801, \cdot)\)	2550.2.c.a	2	1
		2550.2.c.b	2
		2550.2.c.c	2
		2550.2.c.d	2
		2550.2.c.e	2
		2550.2.c.f	2
		2550.2.c.g	2
		2550.2.c.h	2
		2550.2.c.i	2
		2550.2.c.j	2
		2550.2.c.k	2
		2550.2.c.l	4
		2550.2.c.m	4
		2550.2.c.n	4
		2550.2.c.o	4
		2550.2.c.p	4
		2550.2.c.q	4
		2550.2.c.r	6
		2550.2.c.s	6
2550.2.d	\(\chi_{2550}(2449, \cdot)\)	2550.2.d.a	2	1
		2550.2.d.b	2
		2550.2.d.c	2
		2550.2.d.d	2
		2550.2.d.e	2
		2550.2.d.f	2
		2550.2.d.g	2
		2550.2.d.h	2
		2550.2.d.i	2
		2550.2.d.j	2
		2550.2.d.k	2
		2550.2.d.l	2
		2550.2.d.m	2
		2550.2.d.n	2
		2550.2.d.o	2
		2550.2.d.p	2
		2550.2.d.q	2
		2550.2.d.r	2
		2550.2.d.s	2
		2550.2.d.t	2
		2550.2.d.u	4
		2550.2.d.v	4
2550.2.f	\(\chi_{2550}(1699, \cdot)\)	2550.2.f.a	2	1
		2550.2.f.b	2
		2550.2.f.c	2
		2550.2.f.d	2
		2550.2.f.e	2
		2550.2.f.f	2
		2550.2.f.g	2
		2550.2.f.h	2
		2550.2.f.i	2
		2550.2.f.j	2
		2550.2.f.k	2
		2550.2.f.l	2
		2550.2.f.m	2
		2550.2.f.n	2
		2550.2.f.o	4
		2550.2.f.p	4
		2550.2.f.q	4
		2550.2.f.r	4
		2550.2.f.s	4
		2550.2.f.t	4
2550.2.i	\(\chi_{2550}(1007, \cdot)\)	n/a	216	2
2550.2.l	\(\chi_{2550}(443, \cdot)\)	n/a	192	2
2550.2.m	\(\chi_{2550}(1849, \cdot)\)	n/a	104	2
2550.2.p	\(\chi_{2550}(1951, \cdot)\)	n/a	116	2
2550.2.q	\(\chi_{2550}(407, \cdot)\)	n/a	216	2
2550.2.t	\(\chi_{2550}(293, \cdot)\)	n/a	216	2
2550.2.u	\(\chi_{2550}(511, \cdot)\)	n/a	320	4
2550.2.v	\(\chi_{2550}(151, \cdot)\)	n/a	224	4
2550.2.x	\(\chi_{2550}(257, \cdot)\)	n/a	432	4
2550.2.ba	\(\chi_{2550}(593, \cdot)\)	n/a	432	4
2550.2.bc	\(\chi_{2550}(49, \cdot)\)	n/a	224	4
2550.2.be	\(\chi_{2550}(409, \cdot)\)	n/a	320	4
2550.2.bf	\(\chi_{2550}(271, \cdot)\)	n/a	352	4
2550.2.bj	\(\chi_{2550}(169, \cdot)\)	n/a	368	4
2550.2.bl	\(\chi_{2550}(7, \cdot)\)	n/a	432	8
2550.2.bn	\(\chi_{2550}(401, \cdot)\)	n/a	912	8
2550.2.bp	\(\chi_{2550}(299, \cdot)\)	n/a	864	8
2550.2.bq	\(\chi_{2550}(193, \cdot)\)	n/a	432	8
2550.2.bt	\(\chi_{2550}(353, \cdot)\)	n/a	1440	8
2550.2.bv	\(\chi_{2550}(203, \cdot)\)	n/a	1440	8
2550.2.bw	\(\chi_{2550}(361, \cdot)\)	n/a	704	8
2550.2.bz	\(\chi_{2550}(259, \cdot)\)	n/a	736	8
2550.2.ca	\(\chi_{2550}(137, \cdot)\)	n/a	1280	8
2550.2.cc	\(\chi_{2550}(47, \cdot)\)	n/a	1440	8
2550.2.ce	\(\chi_{2550}(19, \cdot)\)	n/a	1408	16
2550.2.ch	\(\chi_{2550}(263, \cdot)\)	n/a	2880	16
2550.2.ci	\(\chi_{2550}(53, \cdot)\)	n/a	2880	16
2550.2.cl	\(\chi_{2550}(121, \cdot)\)	n/a	1472	16
2550.2.cn	\(\chi_{2550}(37, \cdot)\)	n/a	2880	32
2550.2.cp	\(\chi_{2550}(29, \cdot)\)	n/a	5760	32
2550.2.cr	\(\chi_{2550}(11, \cdot)\)	n/a	5760	32
2550.2.cs	\(\chi_{2550}(73, \cdot)\)	n/a	2880	32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 2}\)